# On Hardening Problems in Critical Infrastructure Systems

## TL;DR

This paper models interdependent critical infrastructure networks using Boolean logic, formulates entity hardening problems, proves their NP-Completeness, and proposes ILP and heuristic solutions validated on real and simulated data.

## Contribution

It introduces the Implicative Interdependency Model for precise dependency representation and formulates new hardening problems with proven NP-Completeness, along with solution approaches.

## Key findings

- NP-Completeness of the hardening problems established
- An ILP formulation for optimal solutions provided
- A heuristic method's accuracy validated on real and simulated data

## Abstract

The power and communication networks are highly interdependent and form a part of the critical infrastructure of a country. Similarly, dependencies exist within the networks itself. It is essential to have a model which captures these dependencies precisely. Previous research has proposed certain models but these models have certain limitations. The limitations of the aforementioned models have been overcome by the Implicative Interdependency Model, which uses Boolean Logic to denote the dependencies. This paper formulates the Entity Hardening problem and the Targeted Entity Hardening problem using the Implicative Interdependency Model. The Entity Hardening problem describes a situation where an operator, with a limited budget, must decide which entities to harden, which in turn would minimize the damage, provided a set of entities fail initially. The Targeted Entity Hardening problem is a restricted version of the Entity Hardening problem. This problem presents a scenario where, the protection of certain entities is of higher priority. If these entities were to be nonfunctional, the economic and societal damage would be higher when compared to other entities being nonfunctional. It has been shown that both problems are NP-Complete. An Integer Linear Program (ILP) has been devised to find the optimal solution. A heuristic has been described whose accuracy is found by comparing its performance with the optimal solution using real-world and simulated data.